Diagonality Measures of Hermitian Positive-Definite Matrices with Application to the Approximate Joint Diagonalization Problem

In this paper, we introduce properly-invariant diagonality measures of Hermitian positive-definite matrices. These diagonality measures are defined as distances or divergences between a given positive-definite matrix and its diagonal part. We then give closed-form expressions of these diagonality measures and discuss their invariance properties. The diagonality measure based on the log-determinant $\alpha$-divergence is general enough as it includes a diagonality criterion used by the signal processing community as a special case. These diagonality measures are then used to formulate minimization problems for finding the approximate joint diagonalizer of a given set of Hermitian positive-definite matrices. Numerical computations based on a modified Newton method are presented and commented

Copernicus high-resolution layers for land cover classification in Italy

The high-resolution layers (HRLs) are land cover maps produced for the entire Italian territory (approximately 30 million hectares) in 2012 by the European Environment Agency, aimed at monitoring soil imperviousness and natural cover, such as forest, grassland, wetland, and water surface, with a high spatial resolution of 20 m. This study presents the methodologies developed for the production, verification, and enhancement of the HRLs in Italy. The innovative approach is mainly based on (a) the use of available reference data for the enhancement process, (b) the reduction of the manual work of operators by using a semi-automatic approach, and (c) the overall increase in the cost-efficiency in relation to the production and updating of land cover maps. The results show the reliability of these methodologies in assessing and enhancing the quality of the HRLs. Finally, an integration of the individual layers, represented by the HRLs, was performed in order to produce a National High-Resolution Land Cover ma

Single-Trial Classification of Multi-User P300-Based Brain-Computer Interface Using Riemannian Geometry

International audienceThe classification of electroencephalographic (EEG) data recorded from multiple users simultaneously is an important challenge in the field of Brain-Computer Interface (BCI). In this paper we compare different approaches for classification of single-trials Event-Related Potential (ERP) on two subjects playing a collaborative BCI game. The minimum distance to mean (MDM) classifier in a Riemannian framework is extended to use the diversity of the inter-subjects spatio-temporal statistics (MDM-hyper) or to merge multiple classifiers (MDM-multi). We show that both these classifiers outperform significantly the mean performance of the two users and analogous classifiers based on the step-wise linear discriminant analysis. More importantly, the MDM-multi outperforms the performance of the best player within the pair

A Fixed-Point Algorithm for Estimating Power Means of Positive Definite Matrices

International audienceThe estimation of means of data points lying on the Riemannian manifold of symmetric positive-definite (SPD) matrices is of great utility in classification problems and is currently heavily studied. The power means of SPD matrices with exponent p in the interval [-1, 1] interpolate in between the Harmonic (p =-1) and the Arithmetic mean (p = 1), while the Geometric (Karcher) mean corresponds to their limit evaluated at 0. In this article we present a simple fixed point algorithm for estimating means along this whole continuum. The convergence rate of the proposed algorithm for p = ±0.5 deteriorates very little with the number and dimension of points given as input. Along the whole continuum it is also robust with respect to the dispersion of the points on the manifold. Thus, the proposed algorithm allows the efficient estimation of the whole family of power means, including the geometric mean

Adverse reactions of amiodarone

Adverse drug reaction is defined by the World Health Organization as any response to a drug that is noxious and unintended and occurs at a dose normally used in man. Older people are at elevated risk of adverse drug reactions-because of changes in pharmacodynamics, concurrent use of multiple medications and the related drug interactions. However, adverse drug reactions are significantly underestimated in the elderly population that is also exposed to inappropriate drugs. Amiodarone is an antiarrhythmic drug used commonly for the treatment of atrial fibrillation and is increasingly prescribed in older people. While amiodarone is an efficient drug for rhythm control, it's a carrier of different adverse reactions, and pro and cons must be carefully evaluated before its use especially in older people

Multiclass Brain-Computer Interface Classification by Riemannian Geometry

International audienceThis paper presents a new classification framework for brain-computer interface (BCI) based on motor imagery. This framework involves the concept of Riemannian geometry in the manifold of covariance matrices. The main idea is to use spatial covariance matrices as EEG signal descriptors and to rely on Riemannian geometry to directly classify these matrices using the topology of the manifold of symmetric and positive definite (SPD) matrices. This framework allows to extract the spatial information contained in EEG signals without using spatial filtering. Two methods are proposed and compared with a reference method [multiclass Common Spatial Pattern (CSP) and Linear Discriminant Analysis (LDA)] on the multiclass dataset IIa from the BCI Competition IV. The first method, named minimum distance to Riemannian mean (MDRM), is an implementation of the minimum distance to mean (MDM) classification algorithm using Riemannian distance and Riemannian mean. This simple method shows comparable results with the reference method. The second method, named tangent space LDA (TSLDA), maps the covariance matrices onto the Riemannian tangent space where matrices can be vectorized and treated as Euclidean objects. Then, a variable selection procedure is applied in order to decrease dimensionality and a classification by LDA is performed. This latter method outperforms the reference method increasing the mean classification accuracy from 65.1% to 70.2%

Riemannian geometry applied to BCI classification

ISBN 978-3-642-15994-7, SoftcoverInternational audienceIn brain-computer interfaces based on motor imagery, covariance matrices are widely used through spatial filters computation and other signal processing methods. Covariance matrices lie in the space of Symmetric Positives-Definite (SPD) matrices and therefore, fall within the Riemannian geometry domain. Using a differential geometry framework, we propose different algorithms in order to classify covariance matrices in their native space

A Brain-Switch using Riemannian Geometry

International audienceThis paper addresses the issue of asynchronous brain-switch. The detection of a specific brain pattern from the ongoing EEG activity is achieved by using the Riemannian geometry, which offers an interesting framework for EEG mental task classification, and is based on the fact that spatial covariance matrices obtained on short-time EEG segments contain all the desired information. Such a brain-switch is valuable as it is easy to set up and robust to artefacts. The performances are evaluated offline using EEG recordings collected on 6 subjects in our laboratory. The results show a good precision (Positive Predictive Value) of 92% with a sensitivity (True Positive Rate) of 91%